Approximately Symmetric Neural Networks for Quantum Spin Liquids

We propose and analyze a family of approximately symmetric neural networks for quantum spin liquid problems. These tailored architectures are parameter efficient, scalable, and significantly outperform existing symmetry-unaware neural network architectures. Utilizing the mixed-field toric code and PXP Rydberg Hamiltonian models, we demonstrate that our approach is competitive with state-of-the-art tensor network and quantum Monte Carlo methods. Moreover, at the largest system sizes (N=480 for toric code, N=1584 for Rydberg PXP), our method allows us to explore Hamiltonians with sign problems beyond the reach of both quantum Monte Carlo and finite-size matrix-product states. The network comprises an exactly symmetric block following a nonsymmetric block, which we argue learns a transformation of the ground state analogous to quasiadiabatic continuation. Our Letter paves the way toward investigating quantum spin liquid problems within interpretable neural network architectures.